He received his Ph.D. from Wabash College in 1889. having received his B.A. and M.A. earlier at the same institute. He married Lou Beatrice Sims in 1888 and produced with her three sons and three daughters.
While Rose was employed by the national museum, he was an authority on several plants families, including Apiaceae (Parsley Family) and Cactaceae (Cactus Family). He made several field trips to Mexico, and presented specimens to the Smithsonian and the New York Botanical Garden.
With Nathaniel Lord Britton, Rose published many articles on the Crassulaceae. He took a leave of absence from the Smithsonian to do further fieldwork in South America and publish with Britton, the four-volume work, The Cactaceae (1919 - 1923), illustrated by Mary Emily Eaton (1873-1961).
Rose returned to work afterwards at the Smithsonion, making further contributions to Botany.